平面有向图的自动复杂性
Planar digraphs for automatic complexity
摘要：
我们证明了一个非确定性的有限自动机见证了一个词的自动复杂性的有向图总是可以被认为是平面的。在Shallit和Wang研究的全转移函数的情况下，平面性可能失败。令$s_q(n)$为具有非确定性自动复杂度$A_N(x)=q$的长度为$n$的二进制字$x$的数目。我们表明，$s_q$最终是恒定的每个$q$和最终的恒定值的$s_q$是可计算的。
英文摘要：
We show that the digraph of a nondeterministic finite automaton witnessing the automatic complexity of a word can always be taken to be planar. In the case of total transition functions studied by Shallit and Wang, planarity can fail. Let $s_q(n)$ be the number of binary words $x$ of length $n$ having nondeterministic automatic complexity $A_N(x)=q$. We show that $s_q$ is eventually constant for each $q$ and that the eventual constant value of $s_q$ is computable.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
